[a4isms]

A very famous application of QuadTrees was Bill Gosper's HashLife algorithm for computing Conway's Game of Life. The Life universe is implemented as a quadtree, taking advantage of precomputed smaller squares to compute larger squares.

https://en.wikipedia.org/wiki/Hashlife

https://raganwald.com/2017/01/12/time-space-life-as-we-know-...

[tetris11]

Isn't that just quadratic programming?

[a4isms]

I have nothing to say about Quadratic Programming, so you tell me.

What I can say is that every reference I've found to Bill Gosper's algorithm describes the data structure as an immutable quadtree with canonicalized nodes, id est, there is extensive structure sharing in a Game of Life quadtree. That in turn facilitates heavy memoization.

The wikipedia entry for Quad Trees mentions Hashlife explicitly: https://en.wikipedia.org/wiki/Quadtree